The amount of advertising in the world has indeed been snowballing as societies increasingly embrace a more capitalist style of economic organization.
Does 'snowball' collocate with 'amount'?
If you mean to ask whether "amount snowballed", "snowballing amount" and the like are common expressions, then, no. If you want to know whether the two words work together in this sentence, then, yes.
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If you mean to ask whether "amount snowballed", "snowballing amount" and the like are common expressions, then, no. If you want to know whether the two words work together in this sentence, then, yes.